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Chemical processes as well as many non-industrial processes exhibit autocorrelation, for which the above-mentioned control procedures are not suitable. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive model following a heavy tailed distribution. It also presents practical usage of time series control charts on the chemical process of monitoring concentrations. The second part discusses the effect of autocorrelation on the process capability analysis when the observations are made by an autoregressive model of the first order. The process capability indices provide a measure of how a process fits within the specification limits. When calculating indices, it is usual to assume that the process data are independent. The simulation study in this part discusses the effect of a higher autocorrelation order on process capability indices. Copyright © 2021 Inderscience Enterprises Ltd.

The current methods for estimating Process Capability Indices are based on the assumptions of normality and accuracy of process data. Under actual production conditions the data of quality characteristics of the products may be non-normal and/or have imprecise parameters. Therefore, in this paper we propose a new methodology for estimating Process Capability Indices when the data are non-normal and the specification limits are not crisp numbers. The methodology was validated using experimental data. The proposed methodology uses the Clements's method assuming a Burr type XII distribution, whose parameters are estimated through metaheuristic techniques, and considers the obtaining of fuzzy numbers using the statistical inference theory.

Chemical processes as well as many non-industrial processes exhibit autocorrelation, for which the above-mentioned control procedures are not suitable. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive model following a heavy tailed distribution. It also presents practical usage of time series control charts on the chemical process of monitoring concentrations. The second part discusses the effect of autocorrelation on the process capability analysis when the observations are made by an autoregressive model of the first order. The process capability indices provide a measure of how a process fits within the specification limits. When calculating indices, it is usual to assume that the process data are independent. The simulation study in this part discusses the effect of a higher autocorrelation order on process capability indices. Copyright © 2021 Inderscience Enterprises Ltd.

The main objective of the present study is to present the concept of process capability and to focus its significance in pharmaceutical industries. From a practical view point, the control charts (such as X and R hart) sometimes are not convenient summary statistics when hundreds of characteristics in a plant or supply base are considered. In many situations, capability indices can be used to relate the process parameters. The resulting indices are unit less and provide a common, easily understood language for quantifying the performance of a process. Process capability indices (PCIs) are powerful means of studying the process ability for manufacturing a product that meets specifications. Several capability indices including Cp, Cpu, Cpl and Cpk have been widely used in manufacturing industry to provide common quantitative measures on process potential and performance. The formulas for these indices are easily understood and can be directly implemented. A process capability analysis compares the distribution of output from an in-control process to its specifications limits to determine the consistency with which the specifications can be met. The process capability is also having a significant role in pharmaceutical industry. Process capability indices can be a powerful tool by which to ensure drug product quality and process robustness. Determining process capability provides far more insight into any pharmaceutical process performance than simply computing the percentage of batches that pass or fail each year. Keywords: Process capability; Cp/Cpk; Pp/Ppk; Pharmaceutical quality, process robustness, specification

Process capability indices are widely used to check quality standards both at the production level and for business activity. They consider the location and the deviation from specification limits and targets. The literature contains many contributions on this topic both in the univariate and the multivariate context. Motivated by a real semiconductor case study, we discuss the role of rational subgroups and the challenge they present in the computation of capability indices, especially when data refer to lots of products. In addition, our context involves a mix of problems: unilateral specification limit, nonsymmetric distribution of the data, evidence of data from a mixture of distributions, and the need to filter one component of the mixture. After solving the previous issues and because of the peculiar characteristics of semiconductor processes based on the so called “wafers,” we contribute to the literature a proposal on how to compute capability indices in the case of heteroscedastic spatial processes. With a generalized additive model, we show that it is possible to estimate a capability surface that allows the identification of regions expected to not be fully compliant with the desired quality standards.

The main objective of the present study is to present the concept of process capability and to focus its significance in pharmaceutical industries. From a practical view point, the control charts (such as X and R hart) sometimes are not convenient summary statistics when hundreds of characteristics in a plant or supply base are considered. In many situations, capability indices can be used to relate the process parameters. The resulting indices are unit less and provide a common, easily understood language for quantifying the performance of a process. Process capability indices (PCIs) are powerful means of studying the process ability for manufacturing a product that meets specifications. Several capability indices including Cp, Cpu, Cpl and Cpk have been widely used in manufacturing industry to provide common quantitative measures on process potential and performance. The formulas for these indices are easily understood and can be directly implemented. A process capability analysis compares the distribution of output from an in-control process to its specifications limits to determine the consistency with which the specifications can be met. The process capability is also having a significant role in pharmaceutical industry. Process capability indices can be a powerful tool by which to ensure drug product quality and process robustness. Determining process capability provides far more insight into any pharmaceutical process performance than simply computing the percentage of batches that pass or fail each year. Keywords: Process capability; Cp/Cpk; Pp/Ppk; Pharmaceutical quality, process robustness, specification

Process capability indices are widely used to check quality standards both at the production level and for business activity. They consider the location and the deviation from specification limits and targets. The literature contains many contributions on this topic both in the univariate and the multivariate context. Motivated by a real semiconductor case study, we discuss the role of rational subgroups and the challenge they present in the computation of capability indices, especially when data refer to lots of products. In addition, our context involves a mix of problems: unilateral specification limit, nonsymmetric distribution of the data, evidence of data from a mixture of distributions, and the need to filter one component of the mixture. After solving the previous issues and because of the peculiar characteristics of semiconductor processes based on the so called “wafers,” we contribute to the literature a proposal on how to compute capability indices in the case of heteroscedastic spatial processes. With a generalized additive model, we show that it is possible to estimate a capability surface that allows the identification of regions expected to not be fully compliant with the desired quality standards.

This paper offers a review of univariate and multivariate process capability indices (PCIs). PCIs are statistic indicators widely used in the industry to quantify the capability of production processes by relating the variability of the measures of the product characteristics with the admissible one. Univariate PCIs involve single-product characteristics while multivariate PCIs deal with the multivariate case. When analyzing the capability of processes, decision makers of the industry may choose one PCI among all the PCIs existing in the literature depending on different criteria. In this article, we describe, cluster, and discuss univariate and multivariate PCIs. To cluster the PCIs, we identify three classes of characteristics: in the first class, the characteristics related to the information of the process data input are included; the second class includes characteristics related to the approach used to calculate the PCIs; and in the third class, we find characteristics related to the information that the PCIs give. We discuss the strengths and weaknesses of each PCI using four criteria: calculation complexity, globality of the index, relation to proportion of nonconforming parts, and robustness of the index. Finally, we propose a framework that may help practitioners and decision makers of the industry to select PCIs., Peer Reviewed, Postprint (author's final draft)

Process capability indices are widely used in process assessments and in evaluation of decisions for a continuous improvement of quality in manufacturing or service process. This paper provides a brief survey of the main capability indices. The paper also focalizes the process capability indices in order to determine their sensitivity to time changes of the production system, showing some models, which emphasize both structural and random variables in the short or middle-long period of time. Then, we address the choice of suitable indices to make structural changes relying on the data process monitoring “ex post” or, alternatively, in real time when location or dispersion shifts from the target values are pointed out. Models are given and a Monte Carlo study has been perfomed.

Often the quality of a process is determined by several correlated quality characteristics. In such cases the quality characteristic should be treated as a vector and a number of different multivariate process capability indices (MPCI:s) have been developed for such a situation. One of the existing MPCIs described in the literature is based on principal component analysis (PCA). The idea behind this MPCI is to do a PCA and consider only the first few principle components that explain the main part of the variability. Then one of the well-known univariate process capability indices is applied to each selected principle component and thereafter the univariate process capability indices for the selected principle components are combined to one MPCI. In order define this MPCI the tolerance region for the quality characteristic vector is transformed to a separate specification interval for each principal component. Recently it was shown that this transformation of the tolerance region into separate specification intervals is done in an improper way. And it is far from obvious how to obtain the individual specification limits for each selected principal component when the transformation is properly made. This problem gets complicated for 2 principal components and even worse for more than 2 principal components. We propose a new method based on PCA that circumvent these difficulties for the case when the tolerance region is a hyper-rectangular. This method first transforms the original data in a suitable way. Then PCA is done on the transformed data and it is shown that only the first principal component is needed to deem a process as capable or not at a stated significance level. Hence, a multivariate situation is transferred into a univariate situation and well-known theory for univariate process capability indices can be used to draw conclusions about the process capability. The properties of this method are investigated through a simulation study.

The increasing demand and the globalization of the market are leading to increasing levels of quality in production processes, and thus, nowadays, multiple product characteristics must be tested because they are considered critical. In this context, decision makers are forced to interpret a huge amount of quality indicators, when monitoring production processes. This fact leads to a misunderstanding as a result of information overload. The aim of this paper is to help practitioners when monitoring the capability of processes with a huge amount of product characteristics. We propose a methodology that reduces the amount of data in capability analysis by structuring hierarchically the multiple quality indicators obtained in the quality tests. The proposed methodology may help practitioners and decision makers of the industry in three aspects of statistical process monitoring: to identify the part of a complex production process that presents capability problems, to detect worsening over the time in multivariate production processes, and to compare similar production processes. Some illustrative examples based on different kinds of production processes are discussed in order to illustrate the methodology. A case of study based on a real production process of the automotive industry is analyzed using the proposed methodology. We conclude that the proposed methodology reduces the necessary amount of data in capability analysis; and thus, that it provides an added value of great interest for managers and decision makers., Postprint (published version)